The contact stress between subgrade and subgrade plate was regarded as external force to subgrade. The circular subgrade is divided into rings, and supposing that the contact stress on rings is exerted on elastic subgrade sequentially. The potential energy functions of Bossinesq subgrade are derived by using superposition theorem and Bossinesq solution of elastic mechanics. The potential energy functions were given for the whole system of subgrade, subgrade plate and external forces. The displacement and stress state can be calculated with the principle of minimum potential energy through the potential energy function of the whole system.